Heterojunction Bipolar Transistors for High-Frequency Operation

1. D.L. Pulfrey Department of Electrical and Computer Engineering University of British Columbia Vancouver, B.C. V6T1Z4, Canada pulfrey@ece.ubc.ca http://nano.ece.ubc.ca Heterojunction Bipolar Transistors for High-Frequency Operation Day 3A, May 29, 2008, Pisa

2. Outline • What are the important features of HBTs? • What are the useful attributes of HBTs? • What are the determining factors for IC and IB? • Why are HBTs suited to high-frequency operation? • How are the capacitances reduced?

3. Schematic of InGaP/GaAs HBT • Epitaxial structure • Dissimilar emitter and base materials • Highly doped base • Dual B and C contacts • Identify WB and RB

4. e- h+ HETEROJUNCTION BIPOLAR TRANSISTORS • The major development in bipolar transistors (since 1990) • HBTs break the link between NB and  • Do this by making different barrier heights for electrons and holes • NB can reach 1E20cm-3 - this allows reduction of both WB and RB SHBT - this improves fT and fmax • Key feature is the wide-bandgap emitter An example of Bandgap Engineering

5. Selecting an emitter for a GaAs base AlGaAs / GaAs InGaP / GaAs

6. InGaP/GaAs and AlGaAs/GaAs Draw band diagrams for different emitter

7. Preparing to compute IC • Why do we show asymmetrical hemi-Maxwellians?

8. Current in a hemi-Maxwellian Full Maxwellian distribution Counter-propagating hemi-M's for n0=1E19/cm3 What is the current? /1E20

9. Density of states Recall: In 1-D, a state occupies how much k-space? What is the volume in 3-D? If kx and ky (and kz in 3-D) are large enough, k-space is approximately spherical Divide by V (volume) to get states/m3 Use parabolic E-k (involves m*) to get dE/dk Divide by dE to get states/m3/eV

10. Velocities Turn n(E) from previous slide into n(v) dv using *  vR = 1E7 cm/s for GaAs Currents associated with hemi-M's and M's What is Je,total ? = 1E7 A/cm2 for n0=6E18 /cm3

11. Collector current: boundary conditions

12. Reduce our equation-set for the electron current in the base What about the recombination term?

13. Diffusion and Recombination in the base Here, we need: In modern HBTs WB/Le << 1  and is constant

14. Collector current: controlling velocities * Diffusion (and no recombination) in the base: -1 Note: - the reciprocal velocities - inclusion of vR necessary in modern HBTs * Gives limit to validity of SLJ

15. Comparing results • What are the reasons for the difference?

16. Base current: components (iv) • Which IB components do we need to consider?

17. Base current components and Gummel plot IC IC (A/cm2) IB (recombination) IB (injection) VBE (V) • What is the DC gain?

18. Preparing for the high-frequency analysis • Make all these functions of time and solve! • Or, use the quasi-static approximation

19. The Quasi-Static Approximation q(x, y, z, t' ) = f( VTerminals, t') q(x, y, z, t' )  f( VTerminals, t < t')

20. Small-signal circuit components gm= transconductance go = output conductance g= input conductance g12 = reverse feedback conductance

21. Recall g12=dIb/dVce next

22. Small-signal hybrid- equivalent circuit What are the parasitics?

23. HBT Parasitics • CEB and RB2 need explanation

24. Base-spreading resistance y

25. V + + - - Capacitance Generally: 1 Specifically: 2

26. Emitter-base junction-storage capacitance E B C WB2 QNB QNE QNC WB1 + VBE • QE,j is the change in charge entering the device through the emitter and creating the new width of the depletion layer (narrowing it in this example), • in response to a change in VBE (with E & C at AC ground). • It can be regarded as a parallel-plate cap. What is the voltage dependence of this cap?

27. Emitter-base base-storage capacitance: concept E B C QNB QNE QNC + VBE • QE,b is the change in charge entering the device through the emitter and resting in the base (the black electrons), • in response to a change in VBE (with E & C at AC ground). • It’s not a parallel-plate cap, and we only count one carrier.

28. Emitter-base base-storage capacitance: evaluation B QNB For the case of no recombination in the base: n(x) n(WB) x WB What is the voltage dependence of CEB,b ?

29. Base-emitter transit capacitance: evaluation Q = 3q qe = -2q • What are q0 and qd ? • Where do they come from ?

30. fT from hybrid-pi equivalent circuit • g0 and g set to 0 • fT is measured under AC short-circuit conditions. • We seek a solution for |ic/ib|2 that has a single-pole roll-off with frequency. • Why? • Because we wish to extrapolate at -20 dB/decade to unity gain.

31. Extrapolated fT • Assumption: • Conditions: • Current gain: • Extrapolated fT:

32. Improving fT • III-V for high gm • Implant isolation to reduce C • Highly doped sub-collector and supra-emitter to reduce Rec • Dual contacts to reduce Rc • Lateral shrinking to reduce C's

33. Designing for high fT values Why do collector delays dominate ?

34. How does Si get-in on the act?

35. Developing an expression for fmax Assumption and conditions:

36. Improving fmax • Pay even more attention to Rb and C Final HF question: How far behind are Si MOSFETs?

37. HF MOS What is this?